arXiv 2201.073462022-01-03math.GM

涉及素数立方体的Waring-哥德巴赫问题

Problems related to Waring-Goldbach problem involving cubes of primes

Zhichun Zhai

备注：: The idea to write this note was motived when watching the documentary "Chosen by Mathematics" in the Christmas holiday. No rigorous proof was provided. Some problems were raised

摘要：

本文试图了解涉及素数立方体的Waring-哥德巴赫问题的最新进展。特别是，我们要确定是否整数是素数，素数的平方，素数的立方，或一个偶数的立方可以写为四个素数的立方之和。同时，我们也提出了一些可能加深我们对四个素数立方和问题理解的问题。此外，一些例子表明，几乎所有整数的立方都可以写成四个整数的立方之和。

英文摘要：

In this note, we try to understand the recent development on the Waring-Goldbach problem involving cubes of primes. Especially, we want to determine whether integers that are either primes, squares of primes, cubes of primes, or a cube of an even number can be written as the sum of four cubes of primes. Meanwhile, we raise some problems that may deepen our understanding of the problem about the sum of four cubes of primes. Moreover, some examples suggest that almost all the cubes of integers can be written as the sum of cubes of four integers.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。